Low Probability of Intercept Radar

Short Course on Radar and Electronic Warfare

Kyle Davidson

Seeing, without being seen…

• Low probability of intercept radar implies, that due to:– Low peak and average power

– Wide bandwidth

– Frequency or modulation variability

• The radar is difficult to intercept with a passive receiver

• Relies on antenna patterns, scan patterns, and wavefroms

Low Probability of Identification

• A radar that uses a specially emitted waveform intended to prevent a non-cooperative intercept receiver from intercepting and detecting its emission, but if intercepted, makes identification of the emitted waveform modulation and its parameters difficult

LPI – Array Patterns

• Need to reduce the side lobe levels

• Also prevents jamming

Array Amplitude Weighting

• Apply a amplitude distribution to the phased array elements

• Uniform => narrowest beam width

• Binomial => smallest side lobes

• Tschebyscheff => best compromise between side lobes and beam width

• LPI implies side-lobes below -45 dB

Binomial Array

1 + 𝑥 𝑚−1 = 1 + 𝑚 − 1 𝑥 +𝑚 − 1 𝑚 − 2

2!𝑥2 +⋯

M = 1 1

M = 2 1 1

M = 3 1 2 1

M = 4 1 3 3 1

M = 5 1 4 6 4 1

M = 6 1 5 10 10 5 1

⋮M = 10 1 9 36 84 126 126 84 36 9 1

Tschebyscheff Array

• The related polynomials for the array weighting are:

𝑇𝑚 = cos 𝑚 cos−1(𝑧) − 1 ≤ 𝑧 ≤ +1𝑇𝑚 = cosh 𝑚 cosh−1(𝑧) 𝑧 < 1, 𝑧 > +1

• The math is ugly, see “Antenna Theory –Analysis and Design” by Balanis for more details

Scan Patterns

• Raster Scan is very predictable

• LPI generally scan to limit the target illumination time to short, infrequent, and often unpredictable intervals

• Don’t be predictable!

Reducing Peak Power

• Move to a CW signal

𝑃𝑎𝑣𝑔 = 𝑃𝑡𝜏

𝑇

Power Management

• Why transmit at max power all the time?

– Don’t!

• Limit the power to the range and detection requirements

CW Requires Modulation!

• Linear or non-linear frequency modulation

• Phase modulation (PSK and Barker codes)

• Frequency hopping (FSK) and Costas arrays

• Combined frequency and phase modulation (FSK and PSK)

• Noise modulation

Pulse Compression

• Processing gain from matched filter

𝑃𝐺𝑅 =SNRRo𝑆𝑁𝑅𝑅𝑖

• Depends on time-bandwidth product and integration• Probability of detection, false alarm and SNR out are

related through:𝑆𝑁𝑅𝑅𝑜 = 𝐴 + 0.12𝐴𝐵 + 1.7𝐵

𝐴 = ln0.62

𝑃𝑓𝑎

𝐵 = ln𝑃𝑑

1 − 𝑃𝑑

Processing Gain

• For FMCW radars𝑃𝐺𝑅 = 𝑡𝑚Δ𝐹

• For non-coherent integration for 𝑁𝐼intervals the processing gain is increase by

𝑁𝐼

• For phase coded radars𝑃𝐺 = 𝑁𝑐

• where Nc is the number of subcodes

Who Sees Who First?

• Radar maximum detection range:

𝑅𝑚𝑎𝑥 =𝑃𝐶𝑊𝐺𝑡𝐺𝑟𝜆

2𝜎

4𝜋 3𝑘𝑇0𝐹𝑅𝐵𝑅𝑖 𝑆𝑁𝑅𝑅𝑖

1/4

• Interception range

𝑅𝐼𝑚𝑎𝑥=

𝑃𝐶𝑊𝐺𝑡′𝐺𝐼𝜆

2

4𝜋 2𝑘𝑇0𝐹𝐼𝐵𝐼 𝑆𝑁𝑅𝐼𝑖

1/2

LFM Waveform

FMCW Waveform

Barker Code

3 Different LFM Pulses + Jitter

FSK Pulse